2019AJ....158...86M

Transiting planet surveys of recent years like the Kepler and K2 missions have provided a great deal of data for studying the compositional constituents of exoplanets through the relationship between their masses and radii (M-R relation). However, it is often the case that only one of the mass or radius measurement is available for newly discovered planets, which makes it necessary to estimate the M-R relation conditioned on a sample of planets with both masses and radii measurements available but subject to measurement errors. The majority of the statistical models available in the literature on probabilistic M-R relation are based on the assumption that the planetary masses are normally distributed around the means determined by the power law without any justification. Given the power-law relation, using the well known Maximum Entropy Principle, it is shown that the conditional distribution of masses (given radii) follow an exponential distribution where the conditional mean is modeled using a flexible multiple knot-based power-law structure. Parameter estimation is carried out using Bayesian methods that not only account for measurement errors in building the likelihood function, but also perform proper imputation using posterior predictive distributions. Two data sets (from exoplanets.org site) are used to illustrate the flexibility and broad applicability of the proposed model.